Finite Group Databasebeta

← #14430268

Subgroups — #14430268

Order 1920.

776 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#6819C211yesmaximal, characteristic
2#11752484C211yesmaximal, characteristic, complemented
3C5×#5007C211yesmaximal, characteristic, complemented
4C3×#65297C211yesmaximal, characteristic, complemented
5#11749091C212yesmaximal, complemented
6#11748969C212yesmaximal
7#11747440C212yesmaximal, complemented
8#11747187C212yesmaximal, complemented
9#11747000C211yesmaximal, characteristic, complemented
10#11746946C211yesmaximal, characteristic, complemented
11#11746917C211yesmaximal, characteristic, complemented
12#10612695—31nomaximal, Hall
13C2×#6819C2211yescharacteristic
14C3×C4×C5×D4C2211yescharacteristic
15D4×Dic15C2211yescharacteristic
16C4×#1220—21no—
17C2×C4×Dic15—21no—
18#91781C2211yescharacteristic
19#91776C2211yescharacteristic
20#91770—21no—
21#91766—21no—
22C42×D15C2211yescharacteristic
23C4×Dic30C2211yescharacteristic
24C5×#869C2211yescharacteristic
25C3×#4015C2211yescharacteristic
26#91390—21no—
27#91384C2212yes—
28#91383—21no—
29#91347C2212yes—
30#91344—21no—
31#91331—21no—
32C2×#6648C2212yes—
33C5×#832C2212yes—
34C5×#807C2212yes—
35C5×C4⋊(C3⋊C8)C2211yescharacteristic
36C3×#3964C2212yes—
37C3×#3940C2212yes—
38C3×C4⋊#168C2211yescharacteristic
39#90990C2212yes—
40#90985C2212yes—
41#90983C2212yes—
42#90975C2212yes—
43#90974C2212yes—
44#81059—51nomaximal, Hall
45#66062—31no—
46C4×#711—31no—
47C5×#474—31no—
48#65383—31no—
49#65297D311yescharacteristic, complemented
50#65169—32no—
51#65166—32no—
52#65139—31no—
53D5×C4⋊C8—31no—
54#65061—32no—
55#65055—32no—
56C2×C3×C5×D4C2311yescharacteristic
57C22×C3×C4×C5—21no—
58C2×#1220—21no—
59C22×Dic15—21no—
60C22×Dic15—21no—
61#6819—22no—
62#6819Q814yescomplemented
63C2×C4×D15D411yescharacteristic
64C2×C4×D15D411yescharacteristic
65C2×C4×D15C2311yescharacteristic
66C2×Dic30C2311yescharacteristic
67C2×C5×Dic6—21no—
68C2×C3×Dic10—21no—
69C3×C5×C4⋊C4C2311yescharacteristic
70C3×C5×C22⋊C4—21no—
71C3×C42×C5C2311yescharacteristic
72#6719—21no—
73#6714—21no—
74C4⋊Dic15C2311yescharacteristic
75#6712—21no—
76#6712—21no—
77C4×Dic15—21no—
78C4×Dic15—21no—
79C4×Dic15—21no—
80C4×Dic15D411yescharacteristic
81C4×Dic15D411yescharacteristic
82C4×Dic15C2311yescharacteristic
83C5×C4⋊Dic3—21no—
84C5×C4⋊Dic3C2312yes—
85C2×C5×C3⋊C8C2312yes—
86C3×C4⋊Dic5—21no—
87C3×C4⋊Dic5C2312yes—
88C2×C3×#168C2312yes—
89Dic3⋊Dic5—22no—
90#6668—22no—
91#6667—22no—
92Dic3×Dic5—22no—
93#6648—24no—
94#5728—51no—
95C4×#237—51no—
96C3×#476—51no—
97#5091—51no—
98#5007D511yescharacteristic, complemented
99#4860—52no—
100#4857—52no—
101#4851—51no—
102D3×C4⋊C8—51no—
103#4772—52no—
104#4763—52no—
105C2×#711—31no—
106C5×C4⋊Q8—31no—
107C4×C5×D4C2×D311yescharacteristic
108#4092—61no—
109Q8×Dic5—61no—
110D4×Dic5—31no—
111C4×C22⋊D5—61no—
112C2×C4×Dic5—61no—
113C2×C8×D5—32no—
114#4043—61no—
115#4038—31no—
116#4038—32no—
117#4036—32no—
118#4033—31no—
119#4033—61no—
120#4027—61no—
121#4023—61no—
122C42×D5—31no—
123#4015C2×D311yescharacteristic
124C4×Dic10—31no—
125C5×#107—32no—
126C5×C4⋊C8—31no—
127C5×#102—32no—
128#3964C2×D312yes—
129#3950—32no—
130#3948—32no—
131#3946—32no—
132#3942—32no—
133#3940—32no—
134#3940C2×D312yes—
135C4⋊#168C2×D311yescharacteristic
136#3076—151noSylow
137C23×C3×C5—21no—
138C22×D15C2×D411yescharacteristic
139C3×C5×D4—21no—
140C3×C5×D4C2×Q812yes—
141C2×C3×C4×C5—21no—
142C2×C3×C4×C5—42no—
143C2×C3×C4×C5C2×D411yescharacteristic
144C2×C3×C4×C5C2×D411yescharacteristic
145C2×C3×C4×C5C2411yescharacteristic
146#1220—24no—
147C2×Dic15—21no—
148C2×Dic15—24no—
149C2×Dic15—21no—
150C2×Dic15—42no—
151C2×Dic15C2×D411yescharacteristic
152C2×Dic15C2×D411yescharacteristic
153C2×Dic15C2×D411yescharacteristic
154C4×D15—22no—
155C4×D15—41no—
156C4×D15C2×Q812yes—
157C4×D15#4112yes—
158Dic30—21no—
159Dic30C2×Q812yes—
160C2×C5×Dic3—22no—
161C5×Dic6—42no—
162C2×C3×Dic5—22no—
163C3×Dic10—42no—
164C3×#168—22no—
165C5×C3⋊C8—22no—
166C2×#237—51no—
167C3×C4⋊Q8—51no—
168C3×C4×D4C2×D511yescharacteristic
169#946—101no—
170Q8×Dic3—101no—
171D4×Dic3—51no—
172C4×#67—101no—
173C2×C4×Dic3—101no—
174C2×D3×C8—52no—
175#897—101no—
176#892—51no—
177#892—52no—
178#890—52no—
179#887—51no—
180#887—101no—
181#67⋊C4—101no—
182#877—101no—
183C42×D3—51no—
184#869C2×D511yescharacteristic
185C4×Dic6—51no—
186C3×#106—52no—
187C3×C4⋊C8—51no—
188C3×#102—52no—
189#832C2×D512yes—
190#817—52no—
191#816—52no—
192Dic3⋊C8—52no—
193#810—52no—
194#807—52no—
195#807C2×D512yes—
196C4⋊(C3⋊C8)C2×D511yescharacteristic
197C2×C5×Q8—61no—
198C2×C5×D4C22×D311yescharacteristic
199C22×C4×C5—21no—
200C2×C22⋊D5—61no—
201C22×Dic5—61no—
202C22×Dic5—61no—
203#711—34no—
204#711—62no—
205C2×C4×D5—31no—
206C2×C4×D5—31no—
207C2×C4×D5—31no—
208C2×Dic10—21no—
209C2×Dic10—31no—
210C2×C5×C8—32no—
211C5×C4⋊C4—32no—
212C5×C4⋊C4—61no—
213C5×C4⋊C4C22×D311yescharacteristic
214C5×C22⋊C4—21no—
215C42×C5C22×D311yescharacteristic
216C22⋊Dic5—61no—
217#685—62no—
218#685—61no—
219C4⋊Dic5—21no—
220C4⋊Dic5—31no—
221C4⋊Dic5—62no—
222C4⋊Dic5C22×D312yes—
223#683—62no—
224#683—61no—
225#683—61no—
226C4×Dic5—31no—
227C4×Dic5—31no—
228C4×Dic5—31no—
229C4×Dic5—62no—
230C4×Dic5—61no—
231C4×Dic5—61no—
232C4×Dic5—61no—
233C2×#168C22×D312yes—
234C8×D5—64no—
235#533—151no—
236C4×#41—151no—
237#479—152no—
238#478—152no—
239#477—151no—
240#476—51no—
241#475—151no—
242#474—31no—
243#427—152no—
244C2×C4⋊C8—151no—
245#416—152no—
246C22×C3×C5—22no—
247C22×C3×C5—41no—
248C22×C3×C5—41no—
249C22×C3×C5C22×D411yescharacteristic
250C2×D15—21no—
251C2×D15—21no—
252C2×D15C22⋊Q812yes—
253C3×C4×C5—21no—
254C3×C4×C5—41no—
255C3×C4×C5#13512yes—
256C3×C4×C5C22×Q811yescharacteristic
257C3×C4×C5C2×#4111yescharacteristic
258Dic15—22no—
259Dic15—21no—
260Dic15—21no—
261Dic15—41no—
262Dic15C22⋊Q812yes—
263C3×Dic5—42no—
264C5×Dic3—42no—
265C2×C3×Q8—101no—
266C2×C3×D4C22×D511yescharacteristic
267C22×C3×C4—21no—
268C2×#67—101no—
269C22×Dic3—101no—
270C22×Dic3—101no—
271#237—54no—
272#237—102no—
273C2×C4×D3—51no—
274C2×C4×D3—51no—
275C2×C4×D3—51no—
276C2×Dic6—21no—
277C2×Dic6—51no—
278C2×C3×C8—52no—
279C3×C4⋊C4—52no—
280C3×C4⋊C4—101no—
281C3×C4⋊C4C22×D511yescharacteristic
282C3×C22⋊C4—21no—
283C3×C42C22×D511yescharacteristic
284#217—101no—
285(C2×D3)⋊C4—102no—
286(C2×D3)⋊C4—101no—
287C4⋊Dic3—21no—
288C4⋊Dic3—51no—
289C4⋊Dic3—102no—
290C4⋊Dic3C22×D512yes—
291Dic3⋊C4—102no—
292Dic3⋊C4—101no—
293Dic3⋊C4—101no—
294C4×Dic3—51no—
295C4×Dic3—51no—
296C4×Dic3—51no—
297C4×Dic3—102no—
298C4×Dic3—101no—
299C4×Dic3—101no—
300C4×Dic3—101no—
301C2×C3⋊C8C22×D512yes—
302D3×C8—104no—
303C23×C5—21no—
304C22×D5—31no—
305C5×Q8—122no—
306C5×D4—21no—
307C5×D4D3×Q812yes—
308C2×C4×C5—21no—
309C2×C4×C5—42no—
310C2×C4×C5—62no—
311C2×C4×C5D3×D411yescharacteristic
312C2×C4×C5D3×D411yescharacteristic
313C2×C4×C5C23×D311yescharacteristic
314C22⋊D5—64no—
315C2×Dic5—22no—
316C2×Dic5—31no—
317C2×Dic5—31no—
318C2×Dic5—31no—
319C2×Dic5—64no—
320C2×Dic5—61no—
321C2×Dic5—61no—
322C2×Dic5—122no—
323C4×D5—32no—
324C4×D5—32no—
325C4×D5—62no—
326C4×D5—121no—
327Dic10—32no—
328Dic10—42no—
329Dic10—61no—
330C5×C8—62no—
331#168—22no—
332C2×#41—151no—
333C22×C8—152no—
334C4⋊Q8—31no—
335C4⋊Q8—51no—
336#125—152no—
337C22⋊Q8—301no—
338C22⋊Q8—301no—
339C4×Q8—151no—
340C4×Q8—151no—
341C4×Q8—301no—
342C4×Q8—301no—
343C4×D4—151no—
344C4×D4—301no—
345C4×D4—301no—
346C4×D4D3×D511yescharacteristic
347#117—152no—
348#117—151no—
349#117—301no—
350C2×C42—151no—
351C2×C42—301no—
352#107—32no—
353#107—152no—
354#106—52no—
355#106—152no—
356C4⋊C8—31no—
357C4⋊C8—51no—
358C4⋊C8—152no—
359#103—152no—
360#103—152no—
361#102—32no—
362#102—52no—
363C2×C3×C5—42no—
364C2×C3×C5C2×C22⋊Q811yescharacteristic
365C2×C3×C5C2×#13511yescharacteristic
366C2×C3×C5#57511yescharacteristic
367D15—22no—
368C23×C3—21no—
369C22×D3—51no—
370C3×Q8—202no—
371C3×D4—21no—
372C3×D4Q8×D512yes—
373C2×C3×C4—21no—
374C2×C3×C4—42no—
375C2×C3×C4—102no—
376C2×C3×C4D4×D511yescharacteristic
377C2×C3×C4D4×D511yescharacteristic
378C2×C3×C4C23×D511yescharacteristic
379#67—104no—
380C2×Dic3—22no—
381C2×Dic3—51no—
382C2×Dic3—51no—
383C2×Dic3—51no—
384C2×Dic3—104no—
385C2×Dic3—101no—
386C2×Dic3—101no—
387C2×Dic3—202no—
388C4×D3—52no—
389C4×D3—52no—
390C4×D3—102no—
391C4×D3—201no—
392Dic6—42no—
393Dic6—52no—
394Dic6—101no—
395C3×C8—102no—
396C3⋊C8—22no—
397C22×C5—22no—
398C22×C5—41no—
399C22×C5—41no—
400C22×C5C2×D3×D411yescharacteristic
401C2×D5—32no—
402C2×D5—61no—
403C2×D5—61no—
404C4×C5—21no—
405C4×C5—41no—
406C4×C5—122no—
407C4×C5#91612yes—
408C4×C5C2×D3×Q811yescharacteristic
409C4×C5D3×#4111yescharacteristic
410Dic5—32no—
411Dic5—42no—
412Dic5—61no—
413Dic5—61no—
414Dic5—62no—
415Dic5—121no—
416#41—154no—
417#41—302no—
418C2×Q8—61no—
419C2×Q8—101no—
420C2×Q8—151no—
421C2×D4—301no—
422C2×D4C2×D3×D511yescharacteristic
423C22×C4—21no—
424C22×C4—151no—
425C22×C4—151no—
426C22×C4—151no—
427C22×C4—301no—
428C22×C4—301no—
429C2×C8—32no—
430C2×C8—52no—
431C2×C8—304no—
432C4⋊C4—32no—
433C4⋊C4—52no—
434C4⋊C4—61no—
435C4⋊C4—101no—
436C4⋊C4—151no—
437C4⋊C4—301no—
438C4⋊C4—302no—
439C4⋊C4—302no—
440C4⋊C4—301no—
441C4⋊C4C2×D3×D511yescharacteristic
442C22⋊C4—21no—
443C22⋊C4—301no—
444C22⋊C4—302no—
445C22⋊C4—301no—
446C42—151no—
447C42—151no—
448C42—151no—
449C42—301no—
450C42—301no—
451C42—302no—
452C42—301no—
453C42C2×D3×D511yescharacteristic
454C3×C5#307611yescharacteristic, complemented, Hall
455C22×C3—22no—
456C22×C3—41no—
457C22×C3—41no—
458C22×C3C2×D4×D511yescharacteristic
459C2×D3—52no—
460C2×D3—101no—
461C2×D3—101no—
462C3×C4—21no—
463C3×C4—41no—
464C3×C4—202no—
465C3×C4#405812yes—
466C3×C4C2×Q8×D511yescharacteristic
467C3×C4D5×#4111yescharacteristic
468Dic3—42no—
469Dic3—52no—
470Dic3—101no—
471Dic3—101no—
472Dic3—102no—
473Dic3—201no—
474C2×C5—42no—
475C2×C5D3×C22⋊Q811yescharacteristic
476C2×C5C2×#91611yescharacteristic
477C2×C5#577311yescharacteristic
478D5—62no—
479C23—21no—
480C23—151no—
481Q8—122no—
482Q8—152no—
483Q8—202no—
484Q8—301no—
485D4—21no—
486D4—304no—
487D4D15⋊Q812yes—
488C2×C4—21no—
489C2×C4—42no—
490C2×C4—62no—
491C2×C4—102no—
492C2×C4—151no—
493C2×C4—152no—
494C2×C4—152no—
495C2×C4—151no—
496C2×C4—151no—
497C2×C4—304no—
498C2×C4—301no—
499C2×C4—302no—
500C2×C4—301no—
501C2×C4—601no—
502C2×C4—602no—
503C2×C4#679011yescharacteristic
504C2×C4#679011yescharacteristic
505C2×C4C22×D3×D511yescharacteristic
506C8—62no—
507C8—102no—
508C2×C3—42no—
509C2×C3D5×C22⋊Q811yescharacteristic
510C2×C3C2×#405811yescharacteristic
511C2×C3#6611111yescharacteristic
512D3—102no—
513C5#8105911yescharacteristic, complemented, Sylow
514C22—22no—
515C22—41no—
516C22—41no—
517C22—152no—
518C22—301no—
519C22—301no—
520C22C2×#679011yescharacteristic
521C4—21no—
522C4—41no—
523C4—122no—
524C4—152no—
525C4—202no—
526C4—301no—
527C4—302no—
528C4—301no—
529C4—601no—
530C4#9149912yes—
531C4C2×D15⋊Q811yescharacteristic
532C4#9201611yescharacteristic
533C3#1061269511yescharacteristic, complemented, Sylow
534C2—42no—
535C2—302no—
536C2#1175438311yescharacteristic
537C2C2×#9149911yescharacteristic
538C2#1175534911yescharacteristic
subgroupG/H
centerC22C2×#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
prime radicalC2×#6819C22
hypercenterC4×D4D3×D5
hypocenterC3×C5#3076
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #11752484C2semidirect
3. C5×#5007C2semidirect
4. C3×#65297C2semidirect
5. #11749091C2semidirect
7. #11747440C2semidirect
8. #11747187C2semidirect
9. #11747000C2semidirect
10. #11746946C2semidirect
11. #11746917C2semidirect
49. #65297D3semidirect
62. #6819Q8semidirect
98. #5007D5semidirect
454. C3×C5#3076semidirect
513. C5#81059semidirect
533. C3#10612695semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C4×#68192
#117524842
C5×#50072
C3×#652972
#117490912
#117489692
#117474402
#117471872
#117470002
#117469462
#117469172
#106126953
#810595